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Piyush365

Asked: October 5, 2026In: Class 9 Maths

Is there a 4-gon with given side lengths? (i) Recall the following fact about triangles and check it by construction. For given positive numbers a, b, c, is there a triangle whose sides have these lengths? The answer is Yes exactly when the sum of any two numbers is greater than the third. If we arrange the numbers in increasing order (suppose a ≤ b ≤ c), then this amounts to requiring a + b > c. (Hint: Start by drawing a segment of length c.) (ii) Suppose a 4-gon has 2, 5, 11 as three side lengths. Can the length of the fourth side be 100? Can it be 10? Can it be 1? What are the possible lengths of the fourth side? (iii) For given positive numbers a, b, c, d, how will you decide if there is a 4-gon whose sides have these lengths?

(ii) No for 100 and 1; yes for 10. The fourth side x satisfies 11 – (5 + 2) < x < 11 + 5 + 2, meaning 4 < x < 18. (iii) Each side must be strictly less ...